(a) Use the general solution given in Example 4 to solve

Chapter 6, Problem 39E

(choose chapter or problem)

(a) Use the general solution given in Example 4 to solve the IVP

\(4 x^{\prime \prime}+e^{-0.1 t} x=0, \quad x(0)=1, \quad x^{\prime}(0)=-\frac{1}{2}\)

Also use \(J_{0}^{\prime}(x)=-J_{1}(x)\) and \(Y_{0}^{\prime}(x)=-Y_{1}(x)\) along with Table 6.4.1 or a CAS to evaluate coefficients

(b) Use a CAS to graph the solution obtained in part (a) for \(0 \leq t \leq \infty\).

Text Transcription:

4x^prime\prime+e^-0.1tx=0,x(0)=1,x^prime(0)=-frac12

J_0^prim}(x)=-J_1(x)

Y_0^prime(x)=-Y_1(x)

0tinfty